The invention relates to exploring subsurface earth formations for valuable underground resources, and relates specifically to providing synthetic logs, synthetic seismograms and other signals synthetically derived from well logging measurements.
One major approach to exploring subsurface earth formations is seismic exploration, which involves detecting at the surface the reflections of downwardly propagating seismic signals from subsurface seismic reflectors. Typically, an input seismic signal is generated by exploding a dynamite charge at the bottom of a water-filled hole drilled through the weathered layer of the earth formation of interest. The input seismic signal propagates downwardly primarily as a congressional wave, and is partly refracted and partly reflected back toward the surface at each earth formation reflector (interface of two earth formation layers of different physical properties). The reflection of this compressional wave from the reflectors are detected at each of a plurality of geophones which are typically arranged along a line, although other than linear geophone arrays are often used. The detected reflections typically include primary reflections or simply primaries, when the detected wave has travelled along a generally V-shaped path--i.e. directly downwardly to a reflector and then directly upwardly to a geophone, and multiple reflections of simply multiples, when the detected wave has travelled along a generally W-shaped path at least once--i.e. downwardly to a reflector, then upwardly to another reflector, then again downwardly to a reflector, then again upwardly before reaching the geophone. The arrival times of the reflectons at the geophones are processed to compute, for each geophone, how long it would take for an imaginary input seismic signal originating at the geophone to go straight down to each underlying reflector and come straight back to the geophone as a primary reflection. These times are called the two-way traveltimes for a shotpoint at the geophone location, although in practice one could not have a shotpoint (e.g. a dynamite explosion) at the same point where one has a geophone. The arrival times are additionally processed to find the reflection coefficient of each reflector, where the reflection coefficient is a measure of the difference between the acoustic impedance of the two earth formation layers forming the reflector. Acoustic impedance is the product of the density of a layer and the velocity of a sound compressional wave propagating in it. A seismogram trace is then formed by plotting on a two-way traveltime scale the depth of each reflector (as defined by the two-way traveltime associated with it) and the reflection coefficient of that reflector. A number of such seismogram traces, one for each of a number of geophones detecting the same shot, form a seismogram, which typically has twenty-four traces. FIG. 12 illustrates the general shape of a seismogram, although the specific seismogram of FIG. 12 is synthetically derived in accordance with the invention. In FIG. 12, two-way traveltime increases downwardly, each of the vertical traces is a seismogram trace and each of the heavy dark areas of a trace denotes a reflection coefficient and therefore a reflector, with the size of the dark area corresponding to the value of the reflection coefficient. The vertical section of the earth formation which coincides with the line along which the geophones are arranged is called a seismic section. Thus, in FIG. 12 the plane of the figure is the plane of the seismic section and the rows of dark areas of the traces extending laterally across the figure denote reflectors intersected by the seismic section. Seismograms which are derived in this manner, by detecting reflections of sound compressional waves, are called natural seismograms in this specification to distinguish them from synthetic seismograms derived in other ways, as explained below.
Natural seismograms of this type provide a view of the major features of the earth formation traversed by the seismic section, but can not provide a detailed view thereof and are subject to many inaccuracies.
Another major approach to earth formation exploration involves well logging in a borehole drilled into the formation, and provides an accurate, microscopic look at the earth formation, but mainly for the portion adjacent the borehole. Since well logging provides signals which are generally more accurate than those typically provided in seismic exploration, various attempts have been made in the past to exploit this accuracy in enhancing natural seismograms. As one example, a well logging measurement called the continuous velocity log has been used to construct a corresponding laboratory model of a borehole. The model has been a physical structure whose acoustic impedance varies along its length in a manner analogous to the variation of acoustic impedance with depth in the earth formation where the continuous velocity log was obtained. For example, the model may be a metal rod of varying diameter, or a hollow tube whose cross-sectional area is varied by inserting plugs, or a rod whose velocity is varied by varying the temperature along its length. Transducers are fitted to one end of the model and are used to feed a simulated input seismic signal into the model and to pick up the reflections thereof from the levels in the model which represent reflectors.
The resulting reflections correspond to the two-way traveltimes discussed above for a single geophone and may be used, together with measured reflection coefficients, to construct a single seismogram trace. The trace is thus synthetically derived from well logging measurements. This synthetic seismogram trace may be compared with a natural seismogram for a seismic section which includes the borehole providing the continuous velocity log. The comparision may be made by appropriately scaling the synthetic seismogram trace and the natural seismogram so they are to the same scale, overlaying the synthetic seismogram trace on the natural seismogram over the corresponding (in location) natural seismogram trace, and noting the differences, if any. The natural seismogram may then be corrected in accordance with the synthetic seismogram trace, which may be assumed to be more accurate since it results from inherently more accurate well logging measurements.
As another example of using well logging measurements to construct a synthetic seismogram trace, the continuous velocity log is replotted as a variable area log, and the depth scale is changed to a two-way traveltime scale. This variable area log is drawn past a photocell circuit which gives a single pulse for each significant change in the plotted variable area log. These pulses are passed through a pulse shaping unit whose characteristics are such that a single pulse input provides an output whose waveform is that of a corresponding seismic signal reflection. The output of this unit thus corresponds to the seismic reflection which would be detected for a shotpoint coinciding with the borehole from which the continuous velocity log is derived, and this is passed through a normal seismic amplifier and recorder. The output is usually recorded on two or more channels to increase the resemblance of the resulting synthetic seismic traces to a natural seismogram, which typically has 24 traces. Corresponding synthetic and natural seismogram traces may then be compared to help make the natural seismogram more accurate, or to help interpret the natural seismogram.
As still another example, digital computers have been used to read a continuous velocity log at discrete, equal time intervals and to then calculate corresponding reflection coefficients at each of the points taken, by supposing that there is a reflector at each point in the borehole where a log measurement is taken. These reflection coefficients (possibly including the effects of multiples) are then convolved with the waveform of a selected imaginary input seismic signal. The resulting waveforms are sampled at the same time intervals as the continuous velocity log. The output can then be plotted to give a single synthetic seismogram trace of the type discussed above, which may be used for the same purposes. See: Geophysical Prospecting, Vol. 8, No. 2, p. 231 (1960); Oil and Gas Journal, Nov. 4, 1974, p. 56. See also U.S. Pat. Nos.: 3,008,120; 3,108,250; 3,142,750; and 3,241,102.
These prior art synthetic seismograms are one-dimensional, in the sense that they simulate the seismogram trace for a single shotpoint which coincides with the borehole from which the logs are derived. When a prior art synthetic seismogram is compared with a natural seismogram, the synthetic seismogram corresponds only to a single trace of the natural seismogram, this single trace being for the shotpoint that coincides with the borehole from which the logs are derived. If the seismic section of interest does not coincide with the borehole, then there is no clear correspondence between the prior art synthetic seismogram trace derived from logging measurements and the natural seismogram for the selected seismic section, because generally there is no trace of the natural seismogram which should be the same as the synthetically derived trace. This is so because most real-life earth formations include reflectors which are not horizontal, but dip with respect to a horizontal plane, and any two seismogram traces for such formation would differ since they are for shotpoints at vertical lines which intersect such dipping reflectors at diffeent depths.
Thus, the prior art techniques for generating a synthetic seismogram trace have been limited to producing traces for shotpoints coinciding only with an actual borehole. It has not been possible with such prior art techniques, therefore, to provide truly two-dimensional seismograms, that is accurate synthetic seismogram traces for shotpoints removed along the surface from an actual borehole. If such truly two-dimensional synthetic seismograms could be produced, they would provide a view of the investigated formation comparable to or better than the view that can be provided by the inherently two-dimensional natural seismograms, since they are based on the more accurate well logging measurements.
The term synthetic seismogram has been sometimes used in a different context: it has been applied to the end product of a process which involves arbitrarily selecting a laboratory geological model of an earth formation, that is, defining arbitrarily the location and reflection coefficient of each reflector of an arbitrary formation, and then constructing a synthetic seismogram which would correspond to the arbitrarily selected laboratory model. This, however, does not involve the direct use of logs derived from a borehole traversing the earth formation which is of interest, and thus does not benefit from the inherent accuracy of well logging measurements.